Miao-Kun Wang

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We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1 − α)G(a,b) < A(a,b) < β T (a,b) + (1 − β)G(a,b) holds for all a,b > 0 with a = b. Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. An optimal double inequality between(More)
In this paper, we find the largest value α and least value β such that the double inequality L α (a,b) < M(a,b) < L β (a,b) holds for all a,b > 0 with a = b. Here, M(a,b) and L p (a,b) are the Neuman-Sándor and p-th generalized logarithmic means of a and b , respectively. Optimal combinations bounds of root-square and arithmetic means for Toader mean, An(More)
In this paper, we find the greatest value α and the least values β , p , q and r in (0,1/2) such that the inequalities L(αa + (1 − α)b,αb + (1 − α)a) < P(a,b) < L(β a + (1 − β)b,β b + (1 − β)a) , H(pa + (1 − p)b, pb + (1 − p)a) > G(a,b) , H(qa + (1 − q)b,qb + (1 − q)a) > L(a,b) , and G(ra + (1 − r)b,rb + (1 − r)a) > L(a,b) hold for all a,b > 0 with a = b.(More)